So the first thing i noticed is youre quoting the 11.9 V reading from your battery tender volt meter. Have you used a dvom across the bat terminals to check the battery no load ( key off) voltage ? Same 11.9v result? Dash volt gauge the same? Just to validate your tender reading.
Forget about the battery tender for the moment. As others have said, a good battery should be 12.4-12.8V depending on its health with no load on it. Starting up the engine using the same dvom on the battery will read a higher voltage at engine idle. How much higher will depend on the voltage regulator setting or type and the alternator health. Generally the charging voltage at the battery should be above 13.5V and can be as high as 14.0 V ‘ish depending again on the voltage regulator and or alternator health. My voltage regulator on my Ford 3G alt is set at 14.5V. You should also check the battery voltage with engine off with the battery loaded and measure the voltage at battery again. Key on and headlights on are a good load test with battery still in car. The engine cranking voltage is the best test. Under load will tell the real story on battery health. You should see loaded voltage about 11-12V. I re-learned this last weekend.
My no load voltage at battery was 12.6V yet when I turned the key, nothing worked, as if the main fuse was blown. I started checking down stream of the battery the first 30 minutes , wasting time!. Then I went back to the battery to measure voltage with about 6 amps load ( key on) at the battery, and discovered the voltage was 2.0V. Loading testing revealed the issue. The battery was dead as a door nail. It was 8.5 years old and owed me nothing.